The 2-\((v,k,\lambda )\)  designs \(\mathcal {D}\)  admitting a flag-transitive
automorphism group \(G\)  have been widely studied by several authors. In 1990,
a classification of those with \(\lambda =1\)  and \(G\nleq A\Gamma L_{1}(q)\) 
was announced by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl
in [1]} and proven in [2]}, [3]}, [4]}, [5]},
[6]}, [7]} and [8]}. Since then a special attention was
given to the case \(\lambda >1\) . A classification of the flag-transitive 2-designs with \(\gcd (r,\lambda )=1\) , \(\lambda >1\)  and \(G\nleq A\Gamma L_{1}(q)\) , where \(r\)  is the replication number of \(\mathcal {D}\) , has been
announced by Alavi, Biliotti, Daneshkakh, Montinaro, Zhou and their
collaborators in [9]} and proven in [10]}, [11]}, [12]},
[13]}, [14]},[15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}
and [26]}. Moreover, recently the flag-transitive 2-designs with \(\lambda =2\)  have been investigated by Devillers, Liang, Praeger and Xia in
[27]}, where it is shown that apart from the two known symmetric 2-\((16,6,2)\)  designs, \(G\)  is primitive of affine or almost simple type.
Moreover, a classification is provided when the socle of \(G\)  is isomorphic
to \(PSL_{n}(q)\trianglelefteq G\)  and \(n\geqslant 3\) .
